Method of producing gears



1 a v 1,647,158 Nov 1927 N. TRBOJEVICH METHOD OF PRODUCING GEARSOriginal Filed Jan. 7. 1924 4 Sheets-Sh'ept 1 Fig.5

Nikola Trbojevich INVENTOR ATTORNEY Nov. 1 1927.

N. TRBOJEVICH METHOD OF PRODUCING GEARS Original Filed. Jan. '7. 1924 4Shets-Sheet 2 Nikola Trbry'evih INVENTOIR 7 ATTORNE Nov. 1 1927.

N. TRBOJEVICH M THOD OF raonucme GEARS Original Filed Jan. '7. 1924 4Sheets-Sheet 3.

4 iIiI v M an Nikola Trbojevih INVENTOR B ATTORNE 4 sheets sheet 4 N.TRBOJEVICH METHOD OF PRODUCING GEARS Original Filed Jan. *7. 1924 Nov.

em Aw mu ll an J 5 3 E EE mh H 1%: mm WH IM WWH km Nikola Trbq'evichINVENTOR BY ibx/ ATTORNEY I Patented Nov. 1, 1927.

UNITED STATES- PATENT- OFFICE.

NIKOLA TRBOJ'EVICH, OF HIGHLAND PARK, MICHIGAN, ASSIGINOR TO GLEASONWORKS, OF ROCHESTER, NEW YORK, A CORPORATION'OF NEW YORK.

METHOD or raonnoine GEARS.

Original application filed January 7, 1924, Serial No. 684,862. Dividedand this application filed January The present invention relates to amethod of roducing gears and particularly to a met od of producing gearshaving long1- tudinally curved teeth.

The purpose of the present invention is to provide a simple andinexpensive method of hobbing curved tooth gears, particularly taperedgears having curved teeth such as form the gear or .wheel member of thepairs .of hyperboloidal gears described in my ap plication No. 684,862,filed January 7, 1924, of which the present application is a divi- Thepresent invention provides a method of bobbing curved tooth gears,particularly gears of the type described in the above mentionedapplication, which will be simple and rapid in operation and ofcomparatively low cost. With the above and other objects in view, thepresent invention resides in certain im- 'provements and in the novelsteps constituting the invention, as will be hereinafter more fullydescribed and pointed out in the 5 appended claims.

In the drawings: I Fig. 1 is a diagrammatic view illustrating the theoryupon which theipresent invention is based;

Fig. 2 is a side elevational view, showing somewhat diagrammatically ahobsuch as might be employed in practising this invention in cuttingengagement with the gear being cut thereby;

Fig. 3 is, a plan view of-the hob and gear shown in Fig. 2; Y

Figs. 4 and 5 are two diagrammatic views illustrating d'ifier'entmethods of positioning the hob for cutting a gear according to thisinvention;;

Figs. 6 and 7 are diagrammatic views illustrative of the method ofpractising this invention;

Fig. 8 is a view development of one showing the pitch cone form of hobcapable of being employed in practising this invention;

'Fi 9 is a diagrammatic plan view of a hobbing machine suitable forpractising thls invention.

Serial No. 81,218.

The present invention is based upon the discovery that curved toothgears and particularly tapered curved-tooth gears may be bobbed in ahobbing-process in which the tool and blank are rotated in continuousintermeshing engagement without imparting the usual rolling motion. .Thegear is bobbed by a timed rotation in engagement with the hob, incombination with a simple relative feeding movement between hob andblank necessary to cutthe teeth on the gear to the required depth. Bydoing away with the rolling motion it is possible to simplify thebobbing machinery and process and to produce gears in a shorter time andmore cheaply. The present invention is particularly applicable to themanufacture of the curved tooth hyperboloidal gear which forms onemember of the pair described in the parent application above referredto. In producing this gear, the hob employed is I formed by gashing athread of the same form as the thread of the worm with which the gear isintended to mesh. In order to understand the principle upon which thisinvention is based, it is necessary first to consider certainmathematical and kinematical pecularities upon which the systemis'founded.

Referring first to Fig. 1. If a cone 13 having a cone 8 isso placed withrespect to an orthogonal system of coordinates XYZ that its axis 10 liesin the XY plane at a distance a from the Z axis, and its apex A is 'alsoat the same distance a from said axis; and if the cone is rotated aboutthat axis Z, then the cone B will envelop a hyperboloid of revolution ofone sheet, 1), the mathematical equation of which is:

touches the generated hyperboloid along a plane curve, in particular,along a hyperbola, the equation of which in a plane parallel to the X2plane is:

a 2 e sits a 608 5 6 sin 5 y==c cos 6 The hyperbola defined by theequations (2) is what is termed in mathematics the characteristic of thesystem, that is, it lies both on the cone B and on the $peratedhyperboloid, at the same time. e angle of obliquity of said by erbola isalso equal-to the cone an 1e 6, w ile its transverse and conjugate ha faxes are 0 sin 6 cos 6 and 0 sin 6 respectively.-

ltis now evident from the above demun stration, that it is both possible(theoretisally) to construct'a-pair of mating gears, the pitch surfacesof which are a cone and a hyperboloidrespectively and also that it ispossible to employ a tool of taper formto produce a h perboloidal gear.To produce a practical yperboloidal geara tool must be emplo ed whosecutting edges are so arranged t at the will out without mutilation teethupon t e blank.

Such a gear may be out by employin a taper hob of the modified involutetype. he method of calculating the tool settings and demonstrating thepractical a plication ofthis method of cutting gears w now be described.In Figs. 2 and 3 are shown two views of a taper hob of the typedescribed in cutting engagement with a gear such as may be produced bythis invention. The

taper hob H has a cone angle 6 referably 30 degrees and a constant lead,t at is, its axial sections are the straight rack elements g. The gear Gto be cut is placed relativel to the hob H in such manner that its axis11 is erpendicular to the axis 12 of the hob, and the shortest distancebetween these two axes is equal to c. It can be proved mathematicallyfrom the equations (1)- and (2) that the orge circle a of the pitch hr-- boloid D as a radius equal to 0 cos 6, w

' e the distance of the characteristic hyperbole f measured from theaxis 11 of the gear G is ual to 0 cos 6 and to a sin 6 whenmeasure fromthe axis 12 of the hob H. (Fig: 3).

Now when the hob and the. gear blank are rotated atth'e proper ratio,the hub will cut lon itudinally curved teeth on the blank and wit outmutilation. This can be demon:

. of contact in strated by studying the nature ofthe' com tact whichtakes place between these two bodies when they are rotated on then axesin intermeshing assume apoint Q. lying on the characteristic hyperbolef, and

the neighborhood of the pemt which is timed relation. In order to studythe nature of this contact, we firstmvestigate the conditions [nee-agreeQ As the hyperboloid D is not developable into a plane, and in order torepresent the neighborhood of the point Q upon a developable surface, wedraw a tangent cone I, touching said hyperboloid internally at andhaving its apex at J on the axis 11 of the gear. Thus, the geometricalconfiguration is of the following form. We have a hyperboloid D and apoint Q lying on it.v

The cones B and I are both tangent to said hyperboloid at Q, the formertouching it externally along the hyperbola and the latter internallyalon a circle m a plane perpendicular to the axis. Therefore, the planeQAJ tangent to the hyperboloid at Q is also tangent to both cones B- andL sides, the first of which, QA, is the pitch 'cone radius 'r ofthe'outer cone B, the second of which, QJ is the pitch cone radius R ofthe inner cone I, which cone is identical with the hyperboloid along anarrow circular strip passing through Q, and the third of which, AJ, 15the apex distance G between the two cones measured inthe common tangentplane. Further, r is perpendicular to C. On the other hand an axialsectionof the hob H along an pitch cone radius or generatrixis the racelement 9 as already stated. I have shown in'my Patent No. 1,465,150 andits companion: Patents 1,465,-

perpendicular to the apex distance C and the hob is provided with athread which is of Archimedean spiral form, the equation of where p is5119' 11 sub'nommlvyor ii us angle, that the longitudinal curves of thefication ofthespiral, and ,'is the vectori matin bevel gear must bemodified'involutes efin'ed bythe equations 4 +p) aha -a as (9+?) 8m awec 4:

where a is thebase radius, and the para-' metric angle. The relationalso exists:

As explained in my former patents referred to, .the modified involute isa curve odontically ,oonjugate toan-YArchimedean spiral and isgeometrically defined as the tangential curve of a common involute of149 and 1,465,151, August 14, 1923, that in a case like this where therack element is abridged involute when the amount of in-' ward ornegative modification isoexactly equal to the base radius of the parentinvolute.

Two series of modified involutes will correctly mesh together if bothare generated by the same rack element (having the same pitch andpressure angle) and if they possess the same amount of modification inabsolute value. Thus an Arc-himedean spiral or a tapered hob of constantpitch, be-

ing an abridged involute having a negative modification equal to itspolar sub-normal, the exact value of which is lead of spiral willcorrectly mesh with extended involutes having a +p modification or withabridged involutes havin a -p modification. It is therefore, possi le toemploy a taper hob of the modified involute type in producing ahyperboloidal gear where the .hob is simply rotated in timed relationwith the blank ,while only a simple feed movement is imparted to cutteeth of'the proper depth on the blank. With this hob two types ofhyperboloidal gears may be constructed, respectivelv designated as theextended and abridged types, both of which are capable of correctlymeshing with a conical screw of constant pitch although the nature ofthe contact is fundamentally difierent in each case as more particularlypointed out in my parentapplication above referred to.

Keeping in mind the above disclosed kinematical laws governing thecorrect engagement of spiral bevel gearing of the modified involutetype, we are now in a position to calculate the proper tooth curves fora hyperboloidal wheel G cut by a taper hob H of the modified involutetype. If we denote the coordinates of the point Q, (Fig. 2) with X, Y,and Z"; these coordinates may be determined from the equation (2) asfollows:

X= r cos 8 Y=ccos6 (7) ever, devised a practical method of calculatingthe gearing and of also accurately determining the characteristic anglesand distances to which the spindles of the hobbing machine must be setto produce such gearing. In order to accomplish this. I usually firststart from the plane development of the curves in the nei hborhood ofthe point Q developed upon tie common tangent plane QAJ.

In producing a. gear G, the cone angle of the hob, the form of geartooth curve (extended or abridged involute), the numbers of threads inthe hob and of teeth in the gear, and the angle AQJ=0 are firstselected. Suppose that it is desired to ro-. duce a gear G having teethof the abri ged involute form, (which type is suitable for the finaldrives of automobiles and trucks) then Fig. 4 represents the tangentplane QAJ. If the angle '0 be assumed (in the conditions illustrated inFigs. 2 and 3, 0=45), and the cone angle of the hob is equal to 8 (inthe preferred case, using an Archimedean spiral hob, 30), the cone angleof the inner cone I may be deter- 4 mined from the following relation:

tan 'y tan 8=cos 0 (8) Now. the number of threads in the hob andthenumber of teeth in the gear, n and a. are known as well as the diametralpitch P or lead of the rack element 9'. Hence, the two base radii, p anda are easily determined, as follows:

In cutting a gear of the abridged type,

C tan 0 (11) C sin 0 (12) The shortest distance 0. between the axes. ofthe hob and gear may be determined from the equation: Y

c O Sm 7 cos 6 Fig. 5 shows a diagram analogous to Fig. 4,represent1nthe conditions existing in cutting a gear of the extended type. Here lthe pitch cone of the blank will be 1n the modification is equal to a+In view of the complete analogy, this iagram requires no separateexplanation.

The hob H employed in the preferred form of my invention is providedwith a number of straight or spiral flutes and is relieved in adirection perpendicular to the side of the cone as shown in my PatentNo. 1,465,151. This hob when employed in producing the wheel of a pairof gears such as described in the parent application No. 684,862, willbe an exact counterpart of the tapered worm with which this gear G isadapted to mesh. If the angle [1 (Figs. 4 and 5) is considerable(greater than 8 or 10) the hob may be prov1ded with spiral flutes,similar to those employed in common spur hobs. Fig. 8 shows the pitchcone development of a tapered hob of constant pitch having spiralflutes. The rack elements 9 all converge in the apex K as in thestraight fluted hobs and the cutting edges are ined up along theArchimedean spiral segments h. The flutes are also Archimedean spiralsh" preferably so arranged that they are perpendicular to the threadspirals at the point L, said point ly-- ing substantiall in the middleof the face of the hob. The polar sub-normal 0f the flutes, p'=KM may becalculated from the SLM triangle, said value being:

where r, is equal to the distance IHJ.

Having determined, as previously ex? in timed relation whi e im arting arelag tive feed movement between t e two until the proper depth of teethis reached. The direction of rotation is the same for hob and blank ifagear of the extended type is being out, an opposite (as shown by thearrows in Figures 6 and 7) if a. gear of the abridgedtype' is being cut.This intermeshtimed rotation and feed movement will be such that in theultimate cutting position, tangent relation with respect to the commontan ent plane QAJ (Figures 6 and 7) alon the ine J A, while the pitchcone'E' of t e hob is tangent to said plane on its Opposite side alongthe line AQ. "The itch cone a exes of the blanlzlandrhob fivillbt anebieat findi- A respectiv y. or't ea ri type-t e istance JA is equalto a-p.When this position has been reached,.the angle JQAwill always be equaltothe angle 0 which value was'used in calculating the cone angle and thebase radius a; Inthe' manner just de scribed, all the teeth of the gearG are fintaking into account the desired ished in onecontinuousoperation, both sidesbeing cut and along their entire lengths.

Gears of the type described may be produced on the same machine which isused for hobbing spiral bevel gears and which is fully described in mycopending application Serial No. 637,372, filed May 7, 1923. In cuttinggears of the type herein described, however, the circular feed of thehob about the apex .is disconnected and the hob instead is fed by handor by power in a direction substantially perpendicular to the commontangent plane. The gear produced by the method of my invention bears thesame relation with respect to a spiral bevel gear as does the commonworm gear to a spur helical gear, that is, it is a worm gearmodification of the bevel gear. 7 a

In Fig. 9 I have illustrated diagrammatically a view of a machinesuitable for practising this invention. This machine is the same asthe'one shown in my above mentioned pending application No. 637,372except that the gear trains serving to rotate the feed cylinder in atimed relation with the gear and. hob spindles are omitted'asunnecessary in practising the present invention.

' The hob 20, which in this case has acone angle of is mounted upon the.hob s indie 21 intersectin the common tangent p one 22 at an angle 0 30so that the side of the hob contacting with the gear blank is alwaysparallel to said tangent plane. The hob spindle 21 is. rotatably mountedin the cutter -head '23 which is longitudinally slidable in ways formedin the top of the cutter base 24. This base 24 is ivotally mounted onthe side of the large cy drica casting or spindle 25 for movement aboutthe'center of the shaft 26 from which the hob is driven. Thus the hob isadjustable both angularly and lontudmally 'with respect to the axis ofthe spindle 25'so that its apex may be brought into any desired positionwith reference to the gear apex.

The spindle 25 is rotatable in the main frame 27 of the machine for thepurpose of adjusting the hob for the angle 0, as previouslyexplained.This adjustment is accomplished by rotatingthe handwheel 28 whichactuates a large worm gear 29 through the worm shaft 30. The worm gear29 is connected to the cylinder 25 by means of three screws 31, theaction of which will be explained presentlg.

The hob is riven from the pulley 32 through a pair of speed change ears33, a pair of miter gears'34, the splm shaft 35, three spur gears 36, 37and 38, the shaft 26 and the pair of bevel gears 89. The ear blank Q ismounted in the work hea 41 which his; longitudinally adjustable in thehorizontaf'ways of the work base 42 and also is angularly adjustablewith respect to the frame. Thus the blank may be properly into fulldepth cuttin ment is imparted between these two mem bers as alreadyexplained. The feeding of the hob into the blank may be accomplisheeither by power or by hand. For hand feed, the hand wheel 53 is providedwhich can rotate through the bevel gears 54 the sleeve 55 which ismounted concentric with the shaft 35 and which has secured to it a spurgear 56. This spur gear 56 engages three spur gears 57 each of which iskeyed to one of the screws 31. These screws 31 are housed in threesuitable bearings 58 formed integral with the worm gear 29. The threescrews.

31 thread into suitable bosses 59 which-are formed integral with thecylinder 25. The worm gear 29 is locked during cutting by the worm 30,while the thrust bearings 58 maintain it in a fixed position inavertical plane. Thus, when the three feed screws 31 are rotated thecylinder 25 carrying with it the hob 20 slowly advances in a directionperpendicular to the tangent plane 23.

From the above description, the operation of the machine will be readilyunderstood. It is obvious that the present invention may be practisedwith machines of various and simpler constructions, especially wheresingle purpose manufacturing is deslred.

' While I have illustrated and described a preferred embodiment of myinvention, it

will be understood that the invention is.

capable of further modification within the limits of the invention andthe scope of the appended claims and this applicat1on is intended tocover any variations, uses, or adaptations of m invention, following, ingeneral, the principles of the'invention and including such departuresfrom the present disclosure as come within known or customarly (practisein gear cutting and may be app is to the essential features hereinbcforeset forth and as fall appended claims.

Having thus described my invention, what I claim-is:

1. The method of producing the finishing cut on the side tooth surfacesof a lon itudinally curved tooth tapered gear whic consists in bringinga tool, having its cutting portions arranged in a continuous thread,engagement with a tapered gear blank and rotatlng said tool incontinuous intermeshing engagement with the blank, while rotating theblank continuplane, so that in finish cutting1 within the limits of theout the whole finis ously on its axis and while maintaining the angularrelation between the blank and tool axes constant so that the toolsweeps out the whole finished tooth surface of the blank.

2. The method of roducing the finishing cut on the side tooth surfacesof a longitudinally curved tooth ta .ered gear which consists inbringing a too havmg its cutting portions arranged in a continuousthread of constant pitch into full depth cutting engagement with atapered gear blank and rotating said tool, in continuous interm''shingengagement with the blank, while (1 rotating the blank continuously onits axis and while maintainin the angular relation between the blank antool axes constant so that the'tool sweeps out the whole finished toothsurface of'the blank.

3. The method of producing a lon 'tudi-' nally curved tooth tapered gearwhic consists in positioning a tool, having its cutting portionsarranged in a continuous thread, and a tapered gear. blank so that theyare tangent to a common plane, rotating the tool and blank inintermeshing timed relation,

while imparting a positive relative feed movement between the tool andblank in a direction substantially perpendicular to said position thetool sweeps out the whole finis ed tooth surface of .the blank.

4. The method of cut on the side toot tudinally curved tooth taperedconsists in bringing a taper ho into full depth cutting engagement witha tapered gear blank and rotating said hob in continuous intermeshingengagement with the blank, while rotating the blank continuously on itsaxis and while maintaining the angular relation between the blank andhob axes constant, so that the hob sweeps out the whole finished toothsurface of the blank.

5. The method of producing a lon itudinally curved tooth tapered gearwhic conroducing the finishing surfaces of a longi-v sists inpositioning a taper hob and a.

car which blank in intermeshing timed relation, while impartin apositive relative feed movement between t e hob and blank in a directionsubstantially perpendicular to said plane, 'so that in finish cuttinposition the hob sweeps l ied tooth surface of t e blank. I

6. The method of producing the finishing cut on the side tooth surfacesof a lon 'tudlnally CHI'VGd'tOOth tapered gear whic consists in bringinga taper hob, whose cuttin portions are arranged in a continuous threa ofconstant pitch, into full depth cutting engagement with a tapered gearblank and rotating said hob in continuous intermeshing enga ementlwiththe blank, while rotating the b ank continuously on its axis and whiletinuous intermeshing timed relation with the blank while maintaining theangular relation between the" tool and blank axes con- 1;. 8. The methodof producing longitudinally curved teeth on the side face of a gearblank which consists in bringing a taper hob into full depth cuttingengagement with the blank with its axis non-intersecting andnonarallel'to the blank axis and-rotating'said ob in continuousinterineshing timed relation with the blank while maintaining theangular relation between thetool and lank axes constant. I

9. The method of roducing longitudinally curved teeth on e side face ofa gear blank which consists in bringing a taper hob, having its cuttingortions arranged in a continuous thread 0 constant pitch, into fulldepth'cutting engagement with the blank with its axis non-intersectingand nonparallel to the blank axis and rotat' said hob in continuousintermeshin time relaangular relation between the tool and ank axesconstant.

10. The method of producing longitudinall curved teeth on the side faceof a ear hla which consists in bringing a taper ob, into full depthcuttin engagement with the blank with its apex 0 set from the blank axisand rotating said-hob in continuous intermeshing timed relation with theblank while maintami the angular relation between the tool an blankaxes,'constant.

lL'The method of roducing longitudinally curved teeth on e side face ofa gear blank whichconsists in bringing a taper hob, having its cuttingportions arranged in a continuous thread of constant pitch, into fulldepth cutting enga ement with the blank with its apex oflset' om theblank axis and rotatingsaidhob in continuous intermeshing timed"relation. with the blank while maintainin the tool an blank axesconstant;

12. The method of producing the finishing cut on theside tooth surfacesof 'a-Qlon itudinally curved tooth tapered gear whic consists inbringing a tool,'which is a counterpart of a mating gear, into fulldepth cutting engagement with the blank with its axis offset from theapex of the blank and rotatconstant pitch, into full depth cut-vparallel to the blank axis and what relation with the blank,;while imparelative feed movement between the tool and meshing timed relationwith'the blank while maintaining the angular relation between the toolandblank axes constant. 7 14. The method of producingla longitudinallycurved tooth gear whic consists in bringing a taper 'hob into full de thcutt' engagement with a'taperedgear lank wit the axis of the hobnon-intersecting and nonti S31 hob in continuous intermeshin tim tionwith the blank while maintainin the angular relation betwen the hob andlank axes constant.

15. The method of producin a longitudinally curved tooth gear whicconsistain bringing a taper hob, having its cutting rtions 1 arranged ina-continuous thre of constant pitch, into full depth cuttin en gagementwith a tapered gear blank wit the e axis of the tool non-inrah-- axis ofthe hob non-intersecting and non- Earallelto the blank axis and rotatinsaid ob in continuous intermeshing time relation with the blank whilemainta' the angular relation between the hob and lank axes constant.

16. The method of producin a longitudinally curved tooth gear whichpositioning a tool, having its cuttin tions arranged in a continuousthrea and a tapered ear blank in tan ential relation with the axis ofthe hob extending diagonally of the face of the blank and rotating saidhob in intermeshing timed relation with the blank while imparting arelative feed movement between the hob and blank such that in finishcutting position the angular 'relation between the hob and blank axes ismain-.

tained constant and the hob sweeps out the whole finished toothsurfaceof the blank.-

17 The method of producin a longitudinally curved tooth gear whicconsists" in tions arranged in a continuous thread of constantapitch,and a tapered gear blank in tangent1 relation with the axis of the toolextending diagonally of the face of the blank consists in positioning atool havin its cuttin or: the angular relation between-* g g P a androtatingsaid tool in" intermesh-ing timed rtinga blank such that incutting sitio'n the angular relation between the tool? and blank theblank and rotating said hob in intertapered gear meshing timed relationwith the blank while imparting a relative feed movement between the hoband blank such that in finish cutting osition the angular relationbetween the. hob and blank axes is maintained constant and the hobsweeps out the whole finished tooth surface of the blank.

19. The method of producing a longitudinally curved tooth gear whichconsists in positioning a taper hob,having its cutting portions arrangedin a continuous thread of constant pitch, in tangential relationwith ablank with the axis of the hob extending diagonally of the face of theblank and rotating said hob in intermeshing timed relation with theblank while imparting a relative feed movement between the hob and blanksuch that in finish cutting osition the angular relation of the hob andb ank axes is maintained constant and the hob sweeps out the wholefinished tooth surface of the blank. 20. The method of producing alongitudinally curved tooth gear which consists in positioning a taperhob and a gear blank so that they are tangent to a common plane with theaxis of the hob projected into the tangent pl'anerperpendicular to aline connectmg the hob and ear apexes and rotating the hob and blan inintermeshing timed relation while imparting a positive relative feedmovement between the hob and blank 7 in a direction substantiallyperpendicular to said tangent plane so that invfinish cutting positionthehob sweeps out the whole finish tooth surface of the blank.

21. The method of producing a longitudinally curved tooth gear whichconsists in bringing a taper hob and a gear blank into full depthcuttingengagement with the axis of the-hob projected into the plane tangent tothe pitch surfacesvof hob and blank perpendicular to a line connectingthe hob and gear apexes and rotatingthe hob and blank in continuousintermeshing timed relation while maintaining'the angular relationbetween the hob and blank axes constant.

22. The method of producing alongitudinally curved tooth gear whichconsists in bringing a hob, having its cutting portions arranged in athread which in development is an Archimedean spiral, into full depthcutting engagement with a tapered gear blank and rotating the hob andblank in continuous intermeshing timed relation while maintaining theangular relation be tween the hob and blank axes constant.

23. The method of producing a longitudinally curved tooth gear whichconsistsin positioning a hob, having its cutting portions arranged in athread which in development is an Archimedean spiral, and a cuttingengagement-- with a tapered gear blank and rotating, the hob and blankin continuous intermeshing timed relation while maintaining the angularrelation between the hob and blank axes constant.

25. The method of producing a longitudinally curved tooth gear whichconsists in positioning a hob, having its cutting portions arranged in athread which in development is of modified involute form, and a taperedgear blank so that they are tangent to a common plane and rotating thehob and blank in intermeshing timed relation while imparting a positiverelative feed movement between the hob and blank in a directionsubstantially perpendicular to said tangent plane.

26. The method of producing the finishing cut on the side tooth surfacesof a longitudinally curved tooth tapered gear which consists'inemploying a hob of constant pitch, adapted tozrcut two adjacent sidefaces of the gear teeth simultaneously, bringing said hob into fulldepth cutting engagement with the blank with its axis extendingdiagonally across the tooth zone of the blank and rotating said hob incontinuous intermeshing engagement with the blank, while maintainandblank axes constant, so' that the hob i The method of producing a1ongitudi-' sweeps out the whole of two adjacent finished tooth surfacesof the blank.

27 The method of producing the finishing cut -'on the side toothsurfaces of a longitud1- nally curved tooth tapered gear which consistsin employing. a taper hob, which is adapted to cut two adjacent sidefaces of the gear teeth simultaneously, bringing said hob into fulldepth cutting engagementwith the blank with its axis extendin dia onallyacross the tooth zone of the bladli and rotat- -lI1g said hob incontinuous intermeshing engagement with the blank, while maintainin theangular relation between the hob an blank axes constant, so that the hobsweeps out the whole of two adjacent finished tooth surfaces of theblank.

NIKOLA TRBOJEVIGH.

